Maurice “Hank” Greenberg won his day in federal court, ending a nasty, four-year battle with his former company American International Group.

Next up, though, is the state-court version.

A federal jury decided yesterday that AIG’s demands to seize up to $5 billion of Greenberg’s assets to pay new bonuses to its executives were off base, and that the AIG ex-chief didn’t owe his former company anything.

However, AIG intends to jump immediately back into state Supreme Court in Manhattan, where the beleaguered insurer has kept a copy-cat case on the back burner for years on the same issues that were thrown out in the federal trial.

AIG claims that Greenberg’s private offshore company, Starr International Co., was set up in the 1970s as a trust whose assets had been pledged to pay parent company bonuses.

But after a three-week trial loaded with complex trust and estate arguments, the jury of seven women and one man sided with Greenberg, who argued that there was no evidence of any such bonus trust and that the assets belong to Starr and Greenberg.

US District Court Judge Jed Rakoff said he would rule in August whether to reverse the jury’s decision or let it stand, since the jury decision in this case is only advisory.

Lawmakers have criticized AIG for using taxpayer bailout money to pay for its simultaneous legal fights in two courts — state and federal — costing in excess of $100 million. “This is just throwing taxpayer money down the drain to go after claims that have just been thrown out of federal court,” said a source familiar with the case who asked to remain anonymous.